Re: vector quantities and energy

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

Responding to Gary Hamminger John Mallinckrodt wrote:

> I love this kind of "Why ..." question.  I'd begin my answer as I
> always do to such questions by simply saying, "Because *we* say so."
> This answer helps to emphasize that the theories of physics are pure
> fabrications of the human mind, that physics is about constructing
> mathematical algorithms ("models") that mimic the behavior of nature.
>
> I would go on to point out that we would *not* say so, indeed, that
> the energy--defined as *we* have defined it--would simply not appear
> in the lexicon of physics, if we had not found it to be supremely
> "useful." Its "usefulness" is judged by its prominence and the
> frequency with which it appears in our mathematical models and, most
> importantly, the extent to which those models make predictions that
> are borne out by the verdict of nature itself in experiments.
>
> No answer could *really* be complete, however, without engaging in
> something along the lines suggested by John Denker.  It is our nature
> as human beings to want more than purely pragmatic "natural outcome
> prediction algorithms." When a concept is as useful as energy, we just
> can't help but suspect that there has to be a more fundamental "reason"
> lurking in the background, that our "creation" is *really* a "discovery."
>
> Looking for such reasons is, in some sense, nothing more than engaging
> in metaphysical speculation; we don our philosopher hats and wrap our
> mathematical models in the magnificent robes of "theories" that provide
> a unifying viewpoint and a motivation for the math. Nevertheless, we
> can't test our "theories" (in the sense I have used the word here),
> because we can't tug on those robes; we can only test the algorithms
> around which the robes are wrapped.
>
> We have found, however, that the robes are *themselves* very "useful"
> for they have served to guide our attention, to point in directions that
> are likely to be fruitful for further, more careful analysis.  And, of
> course, the usefulness of the robes (which are, again, a creation of
> the human mind) serves only to strengthen our conviction that they
> "really exist."

I agree with the above but I wish comment on the "really exist" part.
An individual scientist and teacher usually does not create concepts,
s/he learns about them. This learning process (while reading a text,
listening to a lecture, working in a lab, discussing at meeting, etc.)
is discovering. And some of us may be lucky to discover a phenomenon,
or a relation, which was never recognized. For example, a new planet,
emission of penetrating particles, the effect of electric current on
magnets, x rays, Ohm's law, etc.

When we discover such things we call them part of reality. The idea
that "our" intellect does both things (inventing useful concepts and
discovering relations between them) is too good to be thrown away.
"We" make theoretical discoveries (predictions) and experimental
discoveries (electro-optical effects of Faraday, Kerr and Pockel).
And we tell kids that discoverers and inventors are social benefactors.
The collective name for what we find to be true in science is physical
*reality*. It does not include phenomena and relations which can be
imagined but not confirmed.

Should I give the net charge in the dielectric part of a capacitor
as an example of pure imagination? Not yet, the work is still in
progress. But the idea that the moon is made of blue cheese is
certainly a good illustration.
                                    Ludwik Kowalski